Background[ edit ] Christiaan Huygens published the first treaties on probability In Europe, the subject of probability was first formally developed in the 16th century with the work of Gerolamo Cardano , whose interest in the branch of mathematics was largely due to his habit of gambling. However, his actual influence on mathematical scene was not great; he wrote only one light tome on the subject in titled Liber de ludo aleae Book on Games of Chance , which was published posthumously in The two initiated the communication because earlier that year, a gambler from Paris named Antoine Gombaud had sent Pascal and other mathematicians several questions on the practical applications of some of these theories; in particular he posed the problem of points , concerning a theoretical two-player game in which a prize must be divided between the players due to external circumstances halting the game. The Latin title of this book is Ars cogitandi, which was a successful book on logic of the time.
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Biography[ edit ] Jacob Bernoulli was born in Basel , Switzerland. But contrary to the desires of his parents,  he also studied mathematics and astronomy.
He traveled throughout Europe from to , learning about the latest discoveries in mathematics and the sciences under leading figures of the time.
During this time he also produced an incorrect theory of comets. His doctoral dissertation Solutionem tergemini problematis was submitted in During this decade, he also began a fertile research career. His travels allowed him to establish correspondence with many leading mathematicians and scientists of his era, which he maintained throughout his life.
He also studied Isaac Barrow and John Wallis , leading to his interest in infinitesimal geometry. Apart from these, it was between and that many of the results that were to make up Ars Conjectandi were discovered. He was appointed professor of mathematics at the University of Basel in , remaining in this position for the rest of his life.
By that time, he had begun tutoring his brother Johann Bernoulli on mathematical topics. The two brothers began to study the calculus as presented by Leibniz in his paper on the differential calculus in " Nova Methodus pro Maximis et Minimis " published in Acta Eruditorum. They also studied the publications of von Tschirnhaus. Jacob collaborated with his brother on various applications of calculus.
The lunar crater Bernoulli is also named after him jointly with his brother Johann. His geometry result gave a construction to divide any triangle into four equal parts with two perpendicular lines.
By he had published important work on infinite series and published his law of large numbers in probability theory.
Mutaxe The art of measuring, as precisely as possible, probabilities of things, with the goal that we would be able always to choose or follow in our judgments and actions that course, which will have been determined to be better, more satisfactory, safer or more advantageous. It was also hoped that the theory of probability could provide comprehensive and consistent method of reasoning, where ordinary reasoning might be overwhelmed by the complexity of the situation. He gives the first non-inductive proof of the binomial expansion for integer exponent using combinatorial arguments. It also addressed problems that today are classified in the twelvefold way and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. He incorporated fundamental combinatorial topics such as his theory of permutations and combinations the aforementioned problems from the twelvefold way as well as those more distantly connected to the burgeoning subject: Preface by Sylla, vii.